As much as we say that things are "random," seldom do phenomena actually live up to that descriptor. In the classical mechanics of our world—composed of macroscale entities built up from large numbers of particles—everything is determined. Everything has a defined history; every event has a cause; every future can be predicted. Indeed, you were "fated" to read this.
Once you dig all the way down to those individual particles, the smallest of the small, things start to look different. The determinism of our world is traded for probability. An undisturbed particle is like a die flying through the air—a blur of spinning possibilities. It exists in a state of many possibilities at once: here/there, fast/slow, left/right. It's only when we disturb the particle somehow, perhaps by measuring it, that it has to choose a set of specific properties. This is the die as it hits the table, settling down on only one of its six or 20 faces.
This face can then be said to be "random." This is the whole weirdness of quantum physics, really.
As one might imagine, this state of affairs makes calculating quantum systems a holy mess. The probabilities for a single particle are one thing, but when a bunch of particles are together interacting—we say that they're correlated—the problems become very, very hard.
The weird random stuff that arises as a bunch of interrelated quantum particles dance and smash into each other can be explained mathematically.
A pair of physicists, Kaspar Sakmann and Mark Kasevich, have found a new way in, however, by simulating the correlated effects of particles in the super-cold atomic state known as Bose-Einstein condensate and offering "first-principle explanations" for their behavior. In other words, the weird random stuff that arises as a bunch of interrelated quantum particles dance and smash into each other can be explained mathematically.
Technically speaking, what we're after are "single shots." It's a simulated sampling of an ultracold quantum system that should reveal its many-particle probability distribution, e.g. on which face a spinning die is most likely to land given a bunch of other interdependent die all spinning together as they fall toward the table. "In a few cases such single shots could be successfully simulated from a given many-body wavefunction, but for realistic time-dependent many-body dynamics this has been difficult to achieve," Sakmann and Kasevich write.
How do they cut through such a profound randomness? Normally, to describe a many-particle system, we'd come up with a many-particle wave equation. Mathematically, quantum particles are described as wave functions which give a certain probability of a particle having a certain observable property, like position or momentum or spin. These functions can also describe many particles at once, so long as they share a quantum state. While this works for a few particles, once you get into larger and larger numbers, the wave function description gets messy.
Sakmann and Kasevich get around this by instead looking at the collection of particles as the product of a bunch of individual wave functions multiplied together. Start with one particle, do a calculation, and then use that calculation in the calculation for the next particle. Chain these all together and you wind up with a much more reasonable description of the system.
"Such calculations have not been previously possible and our method is broadly applicable to many-body systems whose phenomenology is driven by information beyond what is typically available," they write. Using the technique, the physicists were able to predict and explain previously unexplainable fluctuations and vortices in the quantum mosh pit of a many-particle system.
This isn't likely to lead to some huge awesome technological innovation in the near future, but it does offer a new way into some of the strangest and seemingly most unpredictable phenomena in existence. Randomness is that much more elusive.